How do I have the vertices selected below extend to the edge at the far right side?
If your problem of creating several faces is as simple as shown in this picture, my suggestion would be to do this:


select all the vertices you want to form several quadratic faces.
hit F and create an n-gon
hit CTRL T to triangulate the faces, this results in your n-gon being converted to triangular faces.
hit ALT J to convert tris to quads. This tool is then trying to convert the triangles you've previously created into the quadratic faces you've probably wanted. 


(If you end up with something messy from the convert tris to quads function, try to tweak the settings in the toolbar. )